High-dimensional covariance estimation for Gaussian directed acyclic graph models with given order

被引:0
|
作者
Taylor, Jerome [1 ]
Khare, Kshitij [1 ]
机构
[1] Univ Florida, Dept Stat, 102 Griffin Floyd Hall, Gainesville, FL 32603 USA
关键词
Cholesky decomposition; covariance estimation; high-dimensional data;
D O I
10.1002/wics.1468
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
The covariance matrix is a fundamental quantity that helps us understand the nature of relationships among variables in a multivariate data set. Estimating the covariance matrix can be challenging in modern applications where the number of variables is often larger than the number of samples. In this paper, we review methods which tackle this challenge by inducing sparsity in the Cholesky parameter of the inverse covariance matrix. This article is categorized under: Algorithms and Computational Methods > Numerical Methods Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data
引用
收藏
页数:15
相关论文
共 50 条
  • [31] Confidence intervals for high-dimensional inverse covariance estimation
    Jankova, Jana
    van de Geer, Sara
    [J]. ELECTRONIC JOURNAL OF STATISTICS, 2015, 9 (01): : 1205 - 1229
  • [32] Group Lasso Estimation of High-dimensional Covariance Matrices
    Bigot, Jeremie
    Biscay, Rolando J.
    Loubes, Jean-Michel
    Muniz-Alvarez, Lilian
    [J]. JOURNAL OF MACHINE LEARNING RESEARCH, 2011, 12 : 3187 - 3225
  • [33] Robust Shrinkage Estimation of High-Dimensional Covariance Matrices
    Chen, Yilun
    Wiesel, Ami
    Hero, Alfred O., III
    [J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2011, 59 (09) : 4097 - 4107
  • [34] HIGH-DIMENSIONAL SPARSE COVARIANCE ESTIMATION FOR RANDOM SIGNALS
    Nasif, Ahmed O.
    Tian, Zhi
    Ling, Qing
    [J]. 2013 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), 2013, : 4658 - 4662
  • [35] Faster Algorithms for High-Dimensional Robust Covariance Estimation
    Cheng, Yu
    Diakonikolas, Ilias
    Ge, Rong
    Woodruff, David P.
    [J]. CONFERENCE ON LEARNING THEORY, VOL 99, 2019, 99
  • [36] ESTIMATION OF SMOOTH FUNCTIONALS IN HIGH-DIMENSIONAL MODELS: BOOTSTRAP CHAINS AND GAUSSIAN APPROXIMATION
    Koltchinskii, Vladimir
    [J]. ANNALS OF STATISTICS, 2022, 50 (04): : 2386 - 2415
  • [37] HIGH-DIMENSIONAL COVARIANCE MATRICES UNDER DYNAMIC VOLATILITY MODELS: ASYMPTOTICS AND SHRINKAGE ESTIMATION
    Ding, Yi
    Zheng, Xinghua
    [J]. ANNALS OF STATISTICS, 2024, 52 (03): : 1027 - 1049
  • [38] POSTERIOR GRAPH SELECTION AND ESTIMATION CONSISTENCY FOR HIGH-DIMENSIONAL BAYESIAN DAG MODELS
    Cao, Xuan
    Khare, Kshitij
    Ghosh, Malay
    [J]. ANNALS OF STATISTICS, 2019, 47 (01): : 319 - 348
  • [39] LEARNING HIGH-DIMENSIONAL DIRECTED ACYCLIC GRAPHS WITH LATENT AND SELECTION VARIABLES
    Colombo, Diego
    Maathuis, Marloes H.
    Kalisch, Markus
    Richardson, Thomas S.
    [J]. ANNALS OF STATISTICS, 2012, 40 (01): : 294 - 321
  • [40] Estimating high-dimensional directed acyclic graphs with the PC-algorithm
    Seminar für Statistik, ETH Zurich, 8092 Zürich, Switzerland
    [J]. J. Mach. Learn. Res., 2007, (613-636):